System and method for implementing algorithmic correction of image distortion within a fingerprint imaging system

ABSTRACT

A software implemented system and method for algorithmic correction of systematic image distortions within fingerprint imaging systems. The system and method may implement a three dimensional geometric model of a fingerprint imaging system to discover where a configuration prescribed by a conceptual fingerprint imaging system and an actual configuration of a manufactured fingerprint imaging system differ. By describing this difference using the geometric model, images captured by the manufactured fingerprint imaging system can be rectified in operational use to generate rectified images with relatively low amounts of distortion present.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.11/515,912, filed Sep. 6, 2006, which in turn claims priority under 35U.S.C. §119(e) to Provisional Application No. 60/713,765, filed Sep. 6,2005, both of which are hereby incorporated by reference into thepresent application in their entirety.

FIELD OF THE INVENTION

The invention relates generally to software implemented, algorithmiccorrection of image distortions within fingerprint imaging systems.

BACKGROUND OF THE INVENTION

Conventional fingerprint imaging systems may implement distortioncorrection, also known as rectification, to correct for distortion thatmay typically include correction of radial distortions introduced bylenses. Such radial distortions may include barrel and pincushiondistortion. Rectification also may correct for perspectivedistortions—those distortions which may be introduced into an imagingsystem due to the physical relationship between a principle point on thelens (e.g., the iris) and the scene being captured. Some fingerprintimaging systems may rectify radial and perspective correction in thesystem. For example, some conventional systems include hardware that mayrectify radial and perspective distortion. However, other distortionsmay be present within a captured image due to curved surfaces in thelight path. For instance, imaging through glass balls or from thereflection in a hyperbolic minor may introduce distortions in a capturedimage.

Collectively, these types of image distortions may be referred to assystematic imaging distortions. More specifically, systematic imagedistortions may include those distortions caused by surfaces within afingerprint imaging system at which light may be processed (e.g., lenssurfaces, mirror surfaces, other refractive surfaces, other reflectivesurfaces, and/or other surfaces formed by optical elements).

Generally, conventional rectifying solutions share a focus on correctingimages that have been captured with a simple optical configurationwithin a fingerprint imaging system—a system which may include a cameraand a lens that takes images or photographs of a scene in threedimensions. Conventional solutions often fail to address more complexoptical configurations that include optical elements beyond the lens.That is, the simple imaging systems may not compensate for imagescaptured with multiple optical elements, or a more complex opticalelement, in the light path, such as windows, prisms, non-aligned lenses,balls, or other transparent or semi-transparent media or reflectivesurfaces.

Traditionally, attempts to minimize distortion in fingerprint imagingsystems have been conducted during a design phase. Often, an iterativedesign process may be used in which building and analyzing prototypesystems results in the final fingerprint imaging system design. Theresulting design that meets the distortion goals may incorporateallowable tolerances on system components. Often, additional opticalcomponents may be required in the design to correct distortions to anacceptable level.

During manufacturing, fingerprint imaging systems may be built accordingto the final fingerprint imaging system design. Typically, componentsare assembled and during a quality assurance step, the components areadjusted to ensure that the distortions in each manufactured system donot exceed various tolerances. In order ensure that system distortionsdo not exceed these tolerances, optical components of a relatively highquality and expense are often used. For example, to adhere to theoverall system tolerances, the components themselves may be required tobe manufactured with high precision, thereby increasing a cost ofmanufacturing the corresponding optical component.

In some instances a calibration may be implemented to assure that theoptical components are aligned with a predetermined precision (i.e.,within predetermined alignment tolerances). Calibration typicallyinvolves adjusting component locations with respect to one another tocorrect distortion in images captured by the manufactured systems. Thiscalibration step can be rather involved for higher precision fingerprintimaging system designs with relatively tight alignment tolerances.

During operation, performance of a fingerprint imaging system maydegrade over time. Generally, restoring the calibration of a fingerprintimaging system typically includes a physical adjustment of componentswithin the system to correct for image distortions, and to ensure thatthe alignment of the optical components within the fingerprint imagingsystem falls within the predetermined alignment tolerances, which may becostly and/or time consuming. Other drawbacks in conventionalfingerprint imaging systems exist.

SUMMARY

These and other drawbacks are addressed by various embodiments of theinvention.

One aspect of the invention relates to a software implemented system andmethod for algorithmic correction of image distortions, such assystematic distortions, within fingerprint imaging systems. The systemand method may implement a three dimensional geometric model of afingerprint imaging system to discover where a configuration of aconceptual fingerprint imaging system, built according to a systemdesign with no (or substantially no) imperfections, and an actualconfiguration of a manufactured fingerprint imaging system builtaccording to the system design differ. The difference (or differences)between the conceptual fingerprint imaging system and the manufacturedfingerprint imaging system may arise due to imperfections in themanufactured fingerprint imaging system, including imperfections inalignment and/or configuration of the optical elements, andimperfections in the optical elements themselves. By describing thisdifference using the geometric model, systematic distortion caused bythe imperfections within the manufactured fingerprint imaging system maybe corrected for, thereby enabling images captured by the manufacturedfingerprint imaging system to be rectified in operational use to correctfor the systematic distortion to generate rectified images withrelatively low amounts of residual distortion present. Rectifying theimages to remove systematic distortion based on the geometric model,without physically adjusting and/or correcting the manufacturedfingerprint imaging system or its components, enables the manufacturedfingerprint imaging system to be manufactured with relatively lowertolerances, without degrading the precision of the images generated bythe system. This may enable an enhancement in the precision of generatedimages and/or a lower cost for comparable precision.

In a system design phase, a three dimensional geometric model of theconceptual fingerprint imaging system may be determined. This geometricmodel may describe the surfaces in the conceptual fingerprint imagingsystem that transmit, reflect, refract light, and/or otherwise processlight. For example, an optical design tool such as Zemax may provide anability to define such a geometric model as a series of surfaces.

In a manufacturing phase, a fingerprint imaging system may bemanufactured according to the conceptual fingerprint imaging system.Once a fingerprint imaging system is built, a geometric model of thefingerprint imaging system may be determined based on one or more imagesof a predetermined target captured by the fingerprint imaging system.The target may include objects that may be measured with accuracy belowthe tolerance level desired in output images from the fingerprintimaging system. For instance, the target may include a precision glasstarget with dark circles provided at a periodic pitch on a reflectivebackground.

In some embodiments of the invention, determining the geometric model ofthe fingerprint imaging system may include inputting an image of thetarget captured by the fingerprint imaging system, adjusting surfaceparameters that describe the surfaces within the fingerprint imagingsystem at which light may be processed, and returning the actualrelative optical component locations within the manufactured fingerprintimaging system. The surface parameters may describe, for example, alocation of a surface, a directional orientation of a surface, an indexof refraction of an optical element that forms the surface, and/or otherparameters. In some instances, one tool implemented to adjust thesurface parameters may include a merit function that numericallycompares predicted locations of the objects in the target to theobserved locations of the objects in the captured image of the target.

According to various embodiments of the invention, once an image of thetarget is captured using the fingerprint imaging system, the meritfunction may be implemented to compare the conceptual fingerprintimaging system to the fingerprint imaging system. By running a geometricmodel determination method, surface parameters of the geometric modeldescribing the conceptual fingerprint imaging system can be adjusted sothat the relative location of the surfaces in the geometric modeldescribe the surfaces as they are located and formed within themanufactured fingerprint imaging system. The surface parameters may beadjusted until the geometric model predicts an image that adequatelycoincides with image of the target captured by the manufacturedfingerprint imaging system. That is, by adjusting the merit function'svalue toward a predetermined value (e.g., 0), the geometric modeldefining the relative three-dimensional location of the surfaces in themanufactured fingerprint imaging system may become an adequate predictorof how light within the manufactured fingerprint imaging system may beprocessed to generate an image. The surface parameters determined forthe geometric model may then be stored for image rectification.

In operation, a positional relationship between an observed pixel in animage captured by the fingerprint imaging system and a rectified pixelin a rectified image suitable for output and/or further processing maybe determined using the geometric model's surface parameters. Morespecifically, the geometric model may enable ray tracing to be used togenerate one or more rectified pixels based on one or more observedpixels in a captured image. In some instances, an interpolation methodmay be employed to determine the rectified pixels. For example, therelationship between rectified pixel locations and observed pixellocations can be encoded as one or several pre-calculated lookup tableswhich may then be used for real-time image reconstruction.

In some embodiments of the invention, one or both of the observed imageand the rectified image may be analyzed to determine the likelihood thatthe system is still within the tolerances, for the alignment of opticalcomponents within the system as well as the components themselves,specified when the system was manufactured.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an exemplary illustration of a system for determining ageometric model of a fingerprint imaging system, according to someembodiments of the invention.

FIG. 2 is an exemplary illustration of a fingerprint imaging system, inaccordance with some embodiments of the invention.

FIG. 3 is an exemplary illustration of a method of determining ageometric model of a fingerprint imaging system, according to someembodiments of the invention.

FIG. 4 is an exemplary illustration of a captured image and a rectifiedimage generated from the captured image, in accordance with variousembodiments of the invention.

DETAILED DESCRIPTION

FIG. 1 is an exemplary illustration of a system 110 for determining ageometric model of a fingerprint imaging system 112. The geometric modelmay be implemented, by system 110, for example, to rectify imagescaptured by fingerprint imaging system 112. System 110 may includefingerprint imaging system 112, processor 114, and target 116. Althoughprocessor 114 may be illustrated as a single component in FIG. 1, it maybe appreciated that processor 114 may include a plurality of processorsconnected via an operative link. In some embodiments, the plurality ofprocessors may be located centrally in a single location. In otherembodiments, one or more of the plurality of processors may be locatedremotely from each other. The operative link between the plurality ofprocessors may include a communications link, such as a wired, orwireless communications link, and may include a connection establishedover a network, or via a direct connection. Information may pass betweenfingerprint imaging system 112 and processor 114 via an operative link.The information may include control information, geometric modelinformation, setting information, image information, or otherinformation.

FIG. 2 is an exemplary illustration of fingerprint imaging system 112,according to some embodiments of the invention. Fingerprint imagingsystem 112 may include a radiation source 210 and one or more opticalelements. For example, the optical elements may include a prism 212, amirror 214, and a sensor 216. In other embodiments of the invention, theoptical elements may include other types of elements, such as lenses,apertures, and/or other optical elements. Additionally, the variousoptical elements may be arranged in configurations different from theone illustrated in FIG. 2 without departing from the scope of theinvention.

In some embodiments of the invention, light emitted by radiation source210 may be incident on a platen 218 of prism 212 at an angle greaterthan the critical angle of prism 212 such that the light may beinternally reflected from platen 218. At platen 218, a pattern of anobject in contact with platen 218, such as the fingerprints of anindividual holding at least a portion of his/her hand in contact withplaten 218, may be imparted to the light. The light reflected fromplaten 218 may pass out of prism 212 at a prism face 220 and becomeincident on minor 214. The light from prism 212 may be reflected bymirror 214 through a principle point 222 of fingerprint imaging system112 and onto sensor 216. Sensor 216 may include an electronic imagesensor, such as a CMOS chip, a CCD chip, or another image sensor. Thelight incident on sensor 216 may form an image of the object in contactwith platen 218. Sensor 216 may capture the image formed by the light.

It should be appreciated that the embodiment of fingerprint imagingsystem 112 shown in FIG. 2 is provided for illustrative purposes, andthat the invention contemplates the implementation of any arrangement ofoptical components capable of imaging the fingerprints of an individual.For example, fingerprint imaging system 112 may include a finger printimaging system as described in the co-pending U.S. patent applicationSer. No. 11/030,327, which is incorporated herein by reference.

In some embodiments of the invention, fingerprint imaging system 112 maybe built according to a fingerprint imaging system design for aconceptual fingerprint imaging system. As with most manufacturedsystems, the specifications of fingerprint imaging system 112, includingthe location and orientation of optical elements 212, 214 and 216, aswell as optical elements 212, 214, and 216 themselves, may bemanufactured and assembled within predefined tolerances of thespecifications of the conceptual fingerprint imaging system. However,the manufacturing of fingerprint imaging system 112 according to thespecifications may not be perfect. Deviations of fingerprint imagingsystem 112 from the conceptual fingerprint imaging system, evendeviations within the predefined tolerances, may lead to distortion inthe image of the object that is captured by sensor 216.

Returning to FIG. 1, processor 114 may include a model determinationmodule 118 and a rectification module, among other modules. It should beappreciated that the representation of modules 114 and 116 are providedfor illustrative purposes, and that each module may include one or morecomponents that perform the functionalities assigned to modules 114 and116, as well as other functions. Modules 114 and 116 may includecomponents implemented as hardware, software, firmware, a combination ofhardware, software, and/or firmware, as well as in other mediums.

In some embodiments of the invention, model determination module 118 mayoperate to determine a geometric model of fingerprint imaging system112. The geometric model may account for the deviations between thespecifications of fingerprint imaging system 112 and the conceptualfingerprint imaging system. In some instances, model determinationmodule 118 may implement a geometric model determining method such asthe one described in further detail below to determine the geometricmodel.

According to various embodiments of the invention, rectification module120 may operate to rectify images captured by fingerprint imaging system112 in accordance with the geometric model. Rectification module 120 mayuse the geometric model of fingerprint imaging system 112 determined bymodel determination module 118 to rectify the images captured. In someembodiments, rectification module 120 may implement the geometric modelin a bilinear interpolation to rectify captured images.

FIG. 3 illustrates a method 310 of determining a geometric model of afingerprint imaging system, in accordance with some embodiments of theinvention. At a step 312, a conceptual fingerprint imaging system may bedesigned. For example, designing the conceptual fingerprint imagingsystem may include determining the location and orientation of one ormore optical elements within the conceptual fingerprint imaging systemto capture an image. In some embodiments, the one or more opticalelements may include a prism, a mirror, an imaging surface, a lens, abeam splitter, a film, or other optical elements. The location andorientation of the one or more optical elements may be determined tocapture a certain type (or types) of images, such as, for instance, handor finger prints. The conceptual fingerprint imaging system may bedesigned using optical design software such as Zemax that includes raytracing and other optical design capabilities. In one embodiment, theconceptual fingerprint imaging system may include the conceptualfingerprint imaging system for fingerprint imaging system 112 of FIG. 1.

At a step 314, one or more surfaces at which light is processed (e.g.,reflected, refracted, captured, etc.) within the conceptual fingerprintimaging system may be determined. The surfaces may include the surfacesof the optical elements at which light may be processed within thefingerprint imaging system. For example, some embodiments in which theconceptual fingerprint imaging system includes the conceptualfingerprint imaging system for fingerprint imaging system 112 of FIG. 1,the surfaces may include platen 218, prism face 220, mirror 214, andsensor 216.

At a step 316, the location and orientation of the surfaces within theconceptual fingerprint imaging system may be defined in terms of one ormore parameters, such as, for example, surface parameters. The surfaceparameters may describe, for example, a location of a surface, adirectional orientation of a surface, a shape of a surface, an index ofrefraction of an optical element that forms a surface, and/or otherparameters. In combination, the surface parameters may form an initialgeometric model that may describe the conceptual fingerprint imagingsystem. Or, in other words, the initial geometric model would describethe manufactured fingerprint imaging system, if that fingerprint imagingsystem were manufactured to be substantially identical to the conceptualfingerprint imaging system, and included virtually no imperfections inthe configuration of the one or more optical elements and/or the opticalelements themselves.

In some embodiments, the surface parameters may include: three3-dimensional points that may define flat sensor 216, the three pointsmay include two points that define an edge of sensor 216 as a vector anda third point on sensor 216 that does not lie on this edge; a single3-dimensional point that defines the principal point of the imagingsystem; one 3-dimensional point on the surface of mirror 214 and one3-dimensional direction vector that defines a normal to the surface ofmirror 214; the distances from each of three corners on sensor 216 toprism face 220 along the optical path; the intersection vector betweenthe prism face 220 and the platen 218; and the angle between the prismface 220 and the platen 218. These 28 parameters may define the spatialrelationship between platen 218, prism face 220, mirror 214, principalpoint 222, and sensor 216 in three dimensional space. It should beappreciated that in other embodiments alternative parameters may be usedto completely define the relationships of the surfaces (or the opticalcomponents), and that the parameters above are recited for illustrativepurposes.

At a step 318, a target may be imaged by a fingerprint imaging systembuilt according to the design of the conceptual fingerprint imagingsystem. The target may be located at a predetermined imaging locationwith respect to the fingerprint imaging system. The target may includegraphics in which one or more distinguishing points may be emphasizedgraphically. The distinguishing points may include lines, squares,points, circles, rectangles, or any other shape or mark that may begeometrically analyzed to according to the algorithm described herein.The locations and/or distances between the distinguishing points may bemeasured and recorded with some degree of precision prior to step 318,as a reference. It should be appreciated that in order measure and/orrecord the locations and/or distances between the distinguishing points,the same position on each distinguishing point may be identified (e.g.,the center, a common corner, etc.).

In some embodiments of the invention, the target may include target 116of system 110. Target 116 may include a precision target that includesdistinctive objects located in a periodic manner on a reflectivebackground. For example, target 116 may include a chrome on glass targetthat has chrome dots with a diameter of 1.5 mm provided at a 3.0 mmpitch. Target 116 may be mated with platen 218 using an index matchingfluid. Such a target may be commercially available from various sourcesincluding Applied Optics.

At a step 320, an evaluation function may be determined. The evaluationfunction yields values expressing differences between predictionsrelated to a calculated location (or locations) of the image of thetarget based on the conceptual fingerprint imaging system and a measuredlocation (or locations) of the image of the target captured by theactual fingerprint imaging system. The predictions may includepredictions of the location of the images of the distinguishing points,predictions of the distances between the images of the distinguishingpoints, or other predictions. These predictions may be made via a raytracing capability of the optical design software used to designconceptual fingerprint imaging system. More specifically, ray tracingmay be used to predict what the locations of the images of thedistinguishing points, or the distances of the images of thedistinguishing points, would be by tracing light backwards through theconceptual fingerprint imaging system, from the surface in theconceptual fingerprint imaging system wherein the image of the targetwould be captured, through the optical elements in the fingerprintimaging system, to the surface in the conceptual fingerprint imagingsystem where the target would be positioned. The optical design softwaremay leverage surface parameters to trace the light through theconceptual fingerprint imaging system in order to make thesepredictions. Thus, the surface parameters may be parameters of theevaluation functions.

For example, an evaluation function F, may describe a difference betweena predicted distance between two particular distinguishing points,points i and j, for example, and a distance between a captured image ofthe distinguishing point i and a captured image of the distinguishingpoint j, as a function of the points i and j, in which the surfaceparameters (p) are implemented as parameters of F. This evaluationfunction F may be described asd _(i,j) =F(i,j|p).  (1)

Another way of conceptualizing the evaluation function may be as aplurality of evaluation functions, one for each pair of distinguishingpoints in the image of the target, that determines the differencebetween a predicted distance between two or more distinguishing pointsin the captured image, and the measured distance between thecorresponding distinguishing points in the captured image, as a functionof the surface parameters (p). This set of evaluation functions may berepresented as F_(1,2)(p), F_(1,3)(p), . . . , F_(1,n)(p), F_(2,1)(p),F_(2,3)(p), . . . , F_(2,n)(p), . . . , F_(n,n)(p) for distinguishingpoints i=1 to n. Note that F_(i,i)(p) is 0, because the distance betweenany distinguishing point and itself is 0. It should be appreciated thatalternate evaluation functions that describe the performance of thefingerprint imaging system may be implemented.

At a step 322, the actual image of the target captured by thefingerprint imaging system may be measured. Measuring the image of thetarget may include determining the locations of the images of thedistinguishing points and/or measuring the distances between thedistinguishing points within the image. In some embodiments of theinvention in which the target includes circular dots provided at apredetermined pitch, the images may be distorted in the image capturedby the fingerprint imaging system. In such embodiments, circular dotsmay be extracted from the target by implementing an algorithm thatassumes that the circles are ellipses, and determines the centers of theellipses. For example, an algorithm may be implemented that uses asuper-resolution approach to identifying the edges of the ellipses toenable a determination of the centers of the ellipses within anacceptable tolerance. For each pair of ellipses, a distance between thecenters of the ellipses may be determined. For instance, if 100 dotswere identified in the captured image, there are 100*99/2=4,950 dotpairs for which distances may be determined.

Beginning at a step 324, a data-fitting algorithm may be implemented tominimize the evaluation function(s) by adjusting the surface parametersto more accurately represent the actual configuration of the fingerprintimaging system that may include imperfections in the optical elementsand/or their location and/or orientation within the system. Thedata-fitting algorithm may include a known iterative non-lineardata-fitting algorithm, such as a Levenberg-Marquardt algorithm, a GaussNewton algorithm, or another iterative or non-iterative data-fittingalgorithm for linear or non-linear systems. For example, aLevenberg-Marquardt algorithm may be implemented to minimize a metricfunction (S) where the metric function is the sum of the evaluationfunctions. This sum may be represented mathematically as

$\begin{matrix}{{S(p)} = {\sum\limits_{i = 1}^{n}{\sum\limits_{j = 1}^{n}{\left\lbrack {F_{i,j}(p)} \right\rbrack^{2}.}}}} & (2)\end{matrix}$

At the step 324, the value of the metric function may be determined forthe current surface parameters. The value of the metric function mayrepresent a “goodness of a fit” between the current surface parametersand the actual surface parameters of the fingerprint imaging system. Inother words, the metric function may quantify the accuracy with whichthe current surface parameters describe the manner in which light isprocessed within the fingerprint imaging system. In other embodiments,other functions account for differences between the predicted positionsof, or distances between, the distinguishing points of the target andthe values measured in the image of the target. For example, an averageof the evaluation functions may be implemented as the metric function.Other metric functions and evaluation functions may be implemented.

The premise of the Levenberg-Marquardt algorithm and other data-fittingalgorithms may include collecting the overall observed error andadjusting the surface parameters by a certain amount. As may beappreciated by one of ordinary skill in the art, in this algorithm, theamount to adjust the parameters by may be calculated from the gradientof the merit function with respect the each individual surfaceparameter. Thus, larger slopes may elicit larger movements in thesurface parameters.

In some embodiments of the invention, calculating the gradient of afunction that involves many calculations, such as implementing a raytracing program to predict locations of the images of the distinguishingpoints as described above, especially when deriving the derivativesdirectly, may prove to be computationally intractable. In suchembodiments, to calculate such gradients, an automatic differentiationsoftware package named ADOL may be implemented. This program isaccessible from various sources, such as, atwww.math.tu-dresden.de/˜adol-c/and may include a built in a DLLinterface. Basically, ADOL may track a sequence of mathematicalcalculations, one building upon the other and, when the evaluation of afunction is complete, a record of the sequence of calculations may beused (at a given input point) the evaluate the gradient at that point.Using ADOL, the function for which the gradient is being taken may bemulti-variate and very complex, and yet this approach may accuratelyidentify the gradient at the given input point. Thus, to find thegradient of the metric function for a set of parameter values, a callmay be made to calculate the gradient within an ADOL library after themetric function is evaluated at the set of evaluation functions.

At a step 326, the metric function value may be evaluated to determineif the current surface parameters adequately define the configuration ofthe fingerprint imaging system. In some embodiments, the metric functionvalue may be compared to a threshold value at step 326. If the metricfunction value is greater than the threshold value then method 310 mayproceed to a step 328. At the step 328, the surface parameters may beadjusted in accordance with the implemented curve-fitting algorithm.From step 328, method 310 may loop back for another iteration throughsteps 24 and 26. If it is determined at step 326 that the metricfunction value of the current surface parameters adequately define theconfiguration of the fingerprint imaging system (e.g., the metricfunction value is less than the threshold value), then method 310 mayproceed to a step 330. At step 330, the current surface parameters areadopted as the surface parameters of the fingerprint imaging system, andare implemented in a geometric model of the actual fingerprint imagingsystem. The geometric model may then be implemented to rectify imagescaptured by the fingerprint imaging system.

FIGS. 4A and 4B are exemplary illustrations of a captured image 410,captured by a fingerprint imaging system that includes systematicdistortion introduced by imperfections in the fingerprint imagingsystem, and a rectified image 412, generated by rectifying capturedimage 410 based on a geometric model of the fingerprint imaging systemto remove the systematic distortion. The systematic distortions that maybe present within compound lens systems (e.g., barrel distortion,pincushion distortion, etc.) may also be corrected by implementing themethod described above. For example, the geometric model used togenerate rectified image 412 from captured image 410 may be determinedaccording to method 310.

In some embodiments of the invention, based on the geometric model, raytracing software, such as the optical design software discussed above,may be implemented to trace ray paths through the fingerprint imagingsystem from the imaging location within the fingerprint system where thetarget (or other objects to be imaged) are placed to the surface withinthe fingerprint imaging system where the image of the target may becaptured. Based on these ray paths, positional relationships betweenobserved positions of one or more distinguishing points in an image ofan object captured by the fingerprint imaging system and the positionswithin the image that the one or more distinguishing points may havebeen located if substantially no distortion were introduced byimperfections in the fingerprint imaging system can be ascertained withsuitable accuracy. Using these positional relationships, rectifiedpixels in a rectified image may be generated from observed pixels in acaptured image. The rectified image may be suitable for output and/orfurther processing using the geometric model. In short, the geometricmodel may enable ray tracing to be used to generate one or morerectified pixels based on one or more observed pixels in a capturedimage. In some instances, once the initial ray tracing and determinationof the positional relationships, as described above, have beenaccomplished, the positional relationships may be used to employ aninterpolation method to determine the rectified pixels in imagescaptured by the fingerprint imaging system thereafter. For example, thepositional relationships between rectified pixel locations and observedpixel locations can be encoded as one or more pre-calculated lookuptables which may then be used for real-time image reconstruction.

According to various embodiments of the invention, one or both of theobserved image and the rectified image may be analyzed to determine thelikelihood that the system is still producing images with less than apredetermined amount of distortion. For example, in some instances,fingerprint imaging system 112 may be implemented and at various timesafter the initial determination of the geometric model, image target 116may be captured in order to determine a current metric function value.By way of illustration, at a step 332, shown in FIG. 3, a user mayinitiate a re-determination of the geometric model that may cause animage of target 116 to be captured at step 318 of method 310. From step318, method 310 may be followed, as described above, to adjust thesurface parameters within the geometric model, if need.

It may be appreciated that although the invention has been described interms of algorithmic correction of image distortions within fingerprintimaging systems, that this disclosure is not intended as limiting.Accordingly, the software implemented system and method contemplated bythis disclosure may be implemented to correct image distortions withinother optical imaging systems, thereby reducing a cost of providingimaging systems capable of generating images with a predeterminedprecision.

It can thus be appreciated that embodiments of the invention have nowbeen fully and effectively accomplished. The foregoing embodiments havebeen provided to illustrate the structural and functional principles ofthe present invention, and are not intended to be limiting. To thecontrary, the present invention is intended to encompass allmodifications, alterations and substitutions within the spirit and scopeof the appended claims.

What is claimed is:
 1. A method of calibrating a geometric model of afingerprint imaging system, the geometric model defining geometry ofreflective and/or refractive surfaces associated with optical elementswithin the fingerprint imaging system at which light is reflected orrefracted, the geometric model including a plurality of surfaceparameters that specify relative physical positions of reflective and/orrefractive surfaces within the fingerprint imaging system in relation toother reflective and/or refractive surfaces within the fingerprintimaging system in three-dimensional space, the method comprising:capturing an image of a predetermined target with the fingerprintimaging system, the target including distinguishing points provided atpredetermined positions on the target; measuring positions of thedistinguishing points in the captured image of the target; comparing themeasured positions of the distinguishing points in the captured image topositions of distinguishing points predicted according to the geometricmodel of the fingerprint imaging system; and adjusting the surfaceparameters of the geometric model that specify the relative physicalpositions of reflective and/or refractive surfaces associated withoptical elements in the fingerprint imaging system based on thecomparison between the measured positions of the distinguishing pointsand the predicted positions of the distinguishing points withoutmechanically adjusting the relative physical positions of the refractiveand/or reflective surfaces of the optical elements.
 2. The method ofclaim 1, wherein comparing the measured positions of the distinguishingpoints to the predicted positions of the distinguishing points comprisesdetermining evaluation functions that describe a predicted differencebetween measured positions and predicted positions of a set of one ormore distinguishing points, the surface parameters being parameters inthe evaluation functions.
 3. The method of claim 1, wherein comparingthe measured positions of the distinguishing points to the predictedpositions of the distinguishing points comprises determining a value ofa metric function for the surface parameters, wherein the metricfunction describes an accuracy of the geometric model in predicting thepositions of the distinguishing points in the captured image of thetarget as a function of the surface parameters.
 4. The method of claim3, wherein the step of adjusting the surface parameters is performed aspart of a curve-fitting algorithm designed to minimize the metricfunction.
 5. The method of claim 4, wherein the curve-fitting algorithmcomprises an iterative non-linear algorithm.
 6. The method of claim 5,wherein the curve-fitting algorithm comprises a Levenberg-Marquardtalgorithm or a Gauss Newton algorithm.
 7. The method of claim 1, furthercomprising storing the adjusted surface parameters.
 8. The method ofclaim 7, further comprising rectifying an image captured with thefingerprint imaging system based on the adjusted and stored surfaceparameters.
 9. The method of claim 1, wherein the surface parameterscomprise distances from a first reflective or refractive surface to aplurality of locations on a second reflective or refractive surfacewithin the fingerprint imaging system.
 10. The method of claim 1,further comprising predicting positions of the distinguishing points inthe captured image based on ray tracing through the geometric model ofthe fingerprint imaging system.
 11. A method of determining a geometricmodel of a fingerprint imaging system that captures images of an objectlocated in an object plane of the system, the geometric model defininggeometry of reflective and/or refractive surfaces associated withoptical elements within the fingerprint imaging system at which light isreflected or refracted, the images being captured in an imaging plane ofthe system in which an image of the object is formed, the methodcomprising: determining information related to a position of one or moreoptical surfaces within the fingerprint imaging system, wherein the oneor more optical surfaces comprise reflective and/or refractive surfacesassociated with optical elements at which light is reflected orrefracted within the fingerprint imaging system; generating a geometricmodel of the fingerprint imaging system that defines geometric positionsof the one or more optical surfaces that reflect and/or refract lightwithin the fingerprint imaging system in relation to each other, whereina position of a given optical surface is defined within the geometricmodel by one or more surface parameters of the optical surface, the oneor more surface parameters specifying relative physical positions ofreflective and/or refractive surfaces within the fingerprint imagingsystem in relation to other reflective and/or refractive surfaces withinthe fingerprint imaging system in three-dimensional space; determiningone or more evaluation functions of the fingerprint imaging system thatenable prediction of locations of visual information in the image planeof the fingerprint imaging system based on locations of thecorresponding visual information in the object plane of the fingerprintimaging system, wherein the one or more surface parameters areparameters of the one or more evaluation functions; capturing an imagein the image plane of the fingerprint imaging system, wherein thecaptured image is of a predetermined target located at the object planeof the fingerprint imaging system, the target including distinguishingpoints provided at predetermined positions thereon; predicting positionsof the distinguishing points in the captured image of the predeterminedtarget based on the one or more evaluation functions; measuringpositions of the distinguishing points in the captured image of thepredetermined target; comparing the measured positions of thedistinguishing points in the captured image to the predicted positionsof the distinguishing points in the captured image predicted inaccordance with the one or more evaluation functions; and adjusting thesurface parameters in the geometric model of the fingerprint imagingsystem based on the comparison between the measured positions and thepredicted positions of the distinguishing points in the captured imagewithout mechanically adjusting relative physical positions of therefractive and/or reflective surfaces of the optical elements.
 12. Themethod of claim 11, wherein comparing the measured positions of thedistinguishing points to the predicted positions of the distinguishingpoints comprises determining a value of a metric function for thesurface parameters, wherein the metric function describes an accuracy ofthe geometric model in predicting the positions of the distinguishingpoints in the captured image of the target as a function of the surfaceparameters.
 13. The method of claim 12, wherein the step of adjustingthe surface parameters is performed as part of a curve-fitting algorithmdesigned to minimize the metric function.
 14. The method of claim 13,wherein the curve-fitting algorithm comprises an iterative non-linearalgorithm.
 15. The method of claim 14, wherein the curve-fittingalgorithm comprises a Levenberg-Marquardt algorithm or a Gauss Newtonalgorithm.
 16. The method of claim 11, wherein the measured positions ofthe distinguishing points and the predicted positions of thedistinguishing points comprise positions of the distinguishing points inrelation to each other.
 17. The method of claim 11, further comprisingstoring the adjusted surface parameters for rectifying images capturedby the fingerprint imaging system.
 18. A method of calibrating ageometric model of a fingerprint imaging system, the geometric modeldefining geometry of reflective and/or refractive surfaces associatedwith optical elements within the fingerprint imaging system at whichlight is reflected or refracted, including a plurality of surfaceparameters that specify relative physical positions of reflective and/orrefractive surfaces within the fingerprint imaging system in relation toother reflective and/or refractive surfaces within the fingerprintimaging system in three dimensional space, the method comprising:capturing an image of a predetermined target with the fingerprintimaging system, the target including distinguishing points provided atpredetermined positions; predicting positions of one or more of thedistinguishing points in the captured image of the predetermined targetbased on the geometric model; determining, based on a comparison of thecaptured image and the predicted positions of the one or moredistinguishing points, a value of a metric function that describes anaccuracy of the geometric model in defining the geometry of thereflective and/or refractive surfaces associated with optical elementswithin the fingerprint imaging system; and implementing a curve-fittingalgorithm that adjusts the surface parameters of the geometric modelthat define the relative physical positions of reflective and/orrefractive surfaces within the fingerprint imaging system to reduce thevalue of the metric function without mechanically adjusting the relativephysical positions of the refractive and/or reflective surfaces of theoptical elements.
 19. The method of claim 18, wherein the curve-fittingalgorithm comprises an iterative non-linear algorithm.
 20. The method ofclaim 18, wherein the curve-fitting algorithm comprises aLevenberg-Marquardt algorithm or a Gauss Newton algorithm.